Method and device for determining the dependence of a first measuring quantity on a second measuring quantity

ABSTRACT

For determining the dependence of a first measuring quantity (Y) on a second measuring quantity (P) the second measuring quantity (P) is periodically modified with a frequency (f 0 ). The first measuring quantity (Y) changing accordingly is measured. From the obtained measuring signal of the first measuring quantity (Y) the components of the first measuring quantity (Y) are determined with at least a plurality of frequencies. From the components thus determined the first measuring quantity (Y) is reconstructed for at least a plurality of values of the second measuring quantity (P) by signal processing.

BACKGROUND OF THE INVENTION

1. Field

The invention relates to a method for determining the dependence of afirst measuring quantity on a second measuring quantity wherein

(a) the second measuring quantity is periodically modified with afrequency and

(b) the first measuring quantity changing accordingly is measured.

2. State of the Art

One example for the use of the invention is measuring the surface photovoltage of a material as first measuring quantity in dependence on thewavelength of the excitation light as second measuring quantity. Whenthe surface of a semiconductor is exposed to light, a surface photovoltage is generated at the surface of the material, this surface photovoltage being a function of, inter alia, the diffusion length of thecharge carriers in the material and being indicative thereof. Thesurface photo voltage is also a function of the wavelength of theexcitation light. The longer the wavelength of the light, the higher isthe transmission ability of the material for the light and the deeperpenetrates the light into the material. The relationship betweendiffusion length and surface photo voltage is complicated. However, therelationship can be approximately linearized when operating either withconstant intensity of the light or with constant output signal, thatmeans when the measurement is operated at defined operating points. Themeasurement of the surface photo voltage can be used for detectingirregularities of the material, for example of a semiconductor wafer.For this purpose the surface photo voltage of the material isinvestigated point by point throughout the surface of the material.

Through EP-A-0 077 021 an apparatus is known for nondestructivelymeasuring characteristics of a semiconductor wafer by means of aSPV-method. The wafer is irradiated by a pulsated light beam from alight source. The pulse frequency of the light beam is changeable bymeans of an oscillator. The light beam generates a photo voltage at thesurface of the wafer. This photo voltage is picked up by capacitancecoupling by an electrode. For noise suppression the photo voltage pickedup by capacitance coupling is amplified by an lock-in amplifier. Througha signal processing unit the frequency of the oscillator (and thus thepulse frequency of the light beam) is determined and monitored.Furthermore, the signal processing unit determines the measured photovoltage in dependence on the pulse frequency. The pulse frequency iscontinuously increased and the photo voltage is measured. log V_(ph) isshown as a function of log f at a display. At a critical frequency thedependence of the photo voltage on the pulse frequency changes in acharacteristic manner. This critical frequency is indicative of thecarrier lifetime to be measured, the carrier being generated by thelight beam.

U.S. Pat. No. 5,663,657 also discloses a SPV-method for investigating asemiconductor wafer, in which the diffusion length of minority carrieris determined. A region of the wafer is exposed to light of differentwavelength in several steps and the resulting photo voltage is measured.The photo voltage is determined as a function of the penetration depthof the excitation light, the penetration depth being a function of thewavelength of the light.

SUMMARY OF THE INVENTION

The surface photo voltages are very small and subject to strong noise.Therefore, the measuring is effected by means of a “lock-in” technique.The intensity of the excitation light is modulated with a modulationfrequency and modulation phase. This results in a correspondingmodulation of the measuring signal, as far as this results from theexcitation by the light. By Fourier transformation of the measuringsignal the component of the measuring signal is determined, whichcomponent, with regard to the frequency and the phase, corresponds tothe modulation frequency and the modulation phase. Thus, the noise issuppressed such that even a very weak signal can be detected. Then themeasurement is carried out for each investigated point of the materialat various wavelength of the excitation light.

This measuring method takes very long time. When using the lock-intechnique, a certain number of periods of the modulation frequency, forexample five, is required for each measurement. The modulation frequencyis limited by the material: When exposed to light, it takes a certaintime before a state of equilibrium is reached in the material and ameasurement of the surface photo voltage is useful. When the measurementthen has to be carried out for each scanned point of the surface atvarious wavelengths and many points of the surface are to be scanned,this results in a measuring time which is intolerably long. Thus, inpractice, when testing semiconductor wafers by surface photo voltage,only a very restricted number of measuring points are measured at a veryrestricted number of wavelengths.

It is the object of the invention to reduce the measuring time in thesecases and in the case of methods for determining the dependence of afirst measuring quantity (Y) on a second measuring quantity (P), whichmethods have similar problems, noise being suppressed as well.

According to the invention this object is achieved in a method of theabove mentioned type in that

(c) from the obtained measuring signal of the first measuring quantitythe components of the first measuring quantity are determined with atleast a plurality of frequencies and

(d) from the components thus determined the first measuring quantity isreconstructed for at least a plurality of values of the second measuringquantity by signal processing.

Regarding the example of the surface photo voltage, thus, according tothe invention, a modulation of the excitation light is not effected at apredetermined wavelength, which leads to a modulation of the surfacephoto voltage as “first measuring quantity”. The wavelength of theexcitation light is rather varied as “second measuring quantity”periodically throughout a scanning range with a frequency f₀. Thisresults in a periodical measuring signal. The component of the frequencyf₀ and the higher harmonics 2f₀, 3f₀ . . . up to an upper limitfrequency Nf₀ are obtained from this measuring signal. This alsosuppresses noise. Then, by inverse Fourier transformation, the firstmeasuring quantity (for example surface photo voltage), then free fromnoise, can be reconstructed from the thus determined components independence on the second measuring quantity (for example wavelength) forat least a plurality of values of the second measuring quantity.

The photon density of the excitation light as a function of thewavelength can be measured additionally and taken into account in thecalculation. This photon density can possibly by measured once and beingcalibrated. However, a determination of the photon density and of itsdependence on the wavelength can be repeated in certain time intervals,not necessarily with the modulation frequency. However, it is notnecessary to bring this photon density physically to a constant value atthe various measuring points and wavelengths.

A preferred device for carrying out the method is subject matter ofclaim 9.

Modifications of the invention are subject matter of the sub-claims.

THE DRAWINGS

Embodiments of the invention will now be described in greater detailwith reference to the accompanying drawings.

FIG. 1 is a schematic illustration of a device for measuring thedependence of a first measuring quantity (surface photo voltage) on asecond measuring quantity (wavelength of the excitation light).

FIG. 2 is a schematic illustration of a modification of the device ofFIG. 1 having a comb filter.

FIG. 3 shows a modification of the means for periodically varying thesecond measuring quantity, namely the wavelength of the excitationlight.

FIG. 4 shows a further modification of the means for periodicallyvarying the wavelength, namely by means of a graduated filter.

FIG. 5 shows a modification of the embodiment of FIG. 4.

FIG. 6 is a schematic illustration of the measuring signal obtained withthe device of FIG. 1.

FIG. 7 shows the Fourier transform of the measuring signal of FIG. 4.

FIG. 8 shows schematically the dependence of the first measuringquantity Y (surface photo voltage) on the second measuring quantity P(wavelength of the excitation light) reconstructed from the Fouriertransform of FIG. 5.

FIG. 9 shows schematically the components obtained by the modifiedmeasuring arrangement by means of the comb filter for various harmonicwaves of the modulation frequency.

FIG. 10 shows schematically the values of the first measuring quantity(surface photo voltage) reconstructed therefrom for various values ofthe second measuring quantity (wavelength).

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

In FIG. 1 numeral 10 designates a sample table. A sample 12 of asemiconductor material, for example a semiconductor wafer, to beinvestigated is mounted on the sample table 10. A probe 14 serves formeasuring the surface photo voltage SPV in the various measuring pointsof the surface of the sample. The probe 14 measures the surface photovoltage SPV relative to earth. The very weak signal is filtered andamplified by a signal preprocessing unit, which is illustrated here asamplifier 16.

For generating the surface photo voltage SPV an area on the surface ofthe material is illuminated by light. The light is indicated here by alight beam 18. The light is supplied by a monochromator 20. Themonochromator 20 is provided with an optical member 22, for example anoscillating grating, oscillating harmonically with a frequency f₀. Thus,the wavelength λ of the excitation light is varied periodically withthis frequency f₀. The measuring signal thus obtained then approximatelyshows the course of time illustrated in FIG. 4. The measuring signalamplified by the amplifier 16 is applied to Fourier transformation means24. These supply the Fourier transform of the measuring signal. ThisFourier transform is corrected by correcting means 26 with respect tothe frequency response and phase response of the amplifier 16. Thedependence Y(λ) of the first measuring quantity, that means the surfacephoto voltage SPV, on the second measuring quantity, that means thewavelength λ of the excitation light, is obtained from this correctedFourier transform by a signal processing unit 28. This dependence isapplied to an output 30. The dependence thus obtained correspondsapproximately to FIG. 6.

In the modification illustrated in FIG. 2 the measuring signal isapplied to a comb filter 32. The comb filter 32 supplies, with highfilter quality, the various components of the measuring signal (FIG. 4)with the modulation frequency f₀ and the harmonic waves 2f₀, 3f₀ etc.This is schematically illustrated in FIG. 7. From these components,values Y_(n) of the first measuring quantity, for example the surfacephoto voltage, are determined for various discrete values λ_(n) of thesecond measuring quantity A wavelength@ by means of a signal processingunit 34. This is illustrated in FIG. 8. FIG. 9 shows schematically thecomponents obtained by the modified measuring arrangement by means ofthe comb filter for various harmonic waves oft he modulation frequency.FIG. 10 shows schematically the values of the first measuring quantity(surface photo voltage ) reconstructed therefrom for various values ofthe second measuring quantity (wavelength).

In the modification of the measuring arrangement of FIG. 3 theexcitation light having periodically variable wavelength is notgenerated by a monochromator having oscillating optical member as inFIG. 1. Rather there is provided a white light source 36, the light ofwhich is guided through an acousto-optical transmission filter 38. Theacousto-optical transmission filter 38 is controlled by a sine signal,by which the transmission range of the acousto-optical transmissionfilter is varied according to this signal. This results in a periodicalsine-shaped modulation of the wavelength of the light.

FIG. 4 shows schematically an arrangement in which the wavelength of theexcitation light is variable by means of a graduated filter. Thegraduated filter has a space-dependent transmission area. In the case ofFIG. 4 the graduated filter is a disc 40 which is adapted to oscillateabout an axis 42 as indicated by the double arrow. The transmissibilityof the various sectors of the disc is a function of the circumferentialangle. The transmissibility changes from the wavelength λ₁ over acircumferential area to a wavelength λ₂. With an oscillating movementthese areas move from λ₁ to λ₂ relative to the beam of excitationradiation.

In the embodiment of FIG. 5 the transmission areas changes over 180° tothe right and to the left between the wavelengths λ₁ and λ₂. Then thedisc 40 does not have to carry out an oscillating movement but canrotate continuously.

By moving the sample table the sample 12 can be moved relative to theprobe 14 and to the light source 20, 22 and 36, 38, respectively, suchthat various points of the sample can be scanned consecutively.

Whereas the invention is here illustrated and described with referenceto embodiments thereof presently contemplated as the best mode ofcarrying out the invention in actual practice, it is to be understoodthat various changes may be made in adapting the invention to differentembodiments without departing from the broader inventive conceptsdisclosed herein and comprehended by the claims that follow.

What is claimed is:
 1. A method of determining the dependence of alight-induced material characteristic, occurring at a location of asurface of a material when excited by excitation light having awavelength and directed on said location, on said wavelength of saidexcitation light, comprising the steps of: cyclically varying saidexcitation light wavelength in a wavelength range at a wavelengthvariation frequency, measuring said light-induced materialcharacteristic at said location as a function of said excitation lightwavelength to obtain a signal waveform, as a function of time, cyclic atsaid variation frequency, providing harmonic components of said signalwaveform of measured light-induced material characteristic v. time at,at least, a plurality of frequencies, and constructing, by signalprocessing from said components, a function representing the dependenceof said light-induced material characteristic on said excitation lightwavelength.
 2. A method as claimed in claim 1, wherein saidlight-induced material characteristic is surface photo voltage.
 3. Amethod as claimed in claim 1, wherein said excitation light wavelengthis varied, within said wavelength range, in accordance to a sinefunction.
 4. A method as claimed in claim 1, wherein said harmoniccomponents are provided by subjecting said signal waveform of measuredlight-induced material characteristic v. time to a Fourier transform. 5.A method as claimed in claim 6, and further comprising the step ofcorrecting said Fourier transform for frequency and response affectingsaid signal waveform of measured light-induced material characteristicv. time.
 6. A method as claimed in claim 1, wherein the step ofproviding harmonic components of said signal waveform of measuredlight-induced material characteristic v. time comprises applying saidlight induced material characteristic to a comb filter.
 7. A method asclaimed in claim 1, the step of cyclically varying said excitation lightwavelength in a wavelength range comprises: providing a monochromatorhaving an element the position of which determines an output wavelengthof said monochromator, and cyclically varying said output wavelengthdetermining position.
 8. A method as claimed in claim 1, wherein thestep of cyclically varying said excitation light wavelength in awavelength range comprises: passing a beam of white light through anacousto-optical transmission filter, and applying a sine-wave controlsignal to said acousto-optical transmission filter to vary thetransmission wavelength range accordingly.
 9. A method as claimed inclaim 1, wherein the step of cyclically varying said excitation lightwavelength in a wavelength range comprises: passing a beam of whitelight through a graduated transmission filter, and cyclically displacingsaid graduated transmission filter relative to said beam.
 10. A devicedetermining the dependence of a light-induced material characteristic,occurring at a location of a surface of a material when excited byexcitation light having a wavelength and directed on said location, onsaid wavelength of said excitation light, comprising: means forcyclically varying said excitation light wavelength in a wavelengthrange at a wavelength variation frequency, means for measuring saidlight-induced material characteristic at said location as a function ofsaid excitation light wavelength to obtain a signal waveform, as afunction of time, cyclic at said variation frequency, means forproviding harmonic components of said waveform of measured light-inducedmaterial characteristic v. time at, at least, a plurality offrequencies, and signal processing means for constructing, from saidcomponents, a function representing the dependence of said light-inducedmaterial characteristic on said excitation light wavelength.
 11. Adevice as claimed in claim 10, wherein said light-induced materialcharacteristic is surface photo voltage.
 12. A device as claimed inclaim 10, wherein said means for cyclically varying said excitationlight wavelength comprise a monochromator having an element the positionof which determines an output wavelength of said monochromator, andmeans for cyclically varying said output wavelength determiningposition.
 13. A device as claimed in claim 12, wherein said means forproviding harmonic components of said signal waveform of measuredlight-induced material characteristic v. time comprise Fourier transformmeans for subjecting said signal waveform of measured light-inducedmaterial characteristic v. time to a Fourier transform.
 14. A device asclaimed in claim 13, and further comprising means for correcting saidFourier transform for frequency and response affecting said signalwaveform of measured light-induced material characteristic v. time. 15.A device as claimed in claim 10, wherein said means for providingharmonic components of said signal waveform of measured light-inducedmaterial characteristic v. time comprise means for applying said lightinduced material characteristic to a comb filter.
 16. A device asclaimed in claim 10, wherein said means for cyclically varying saidexcitation light wavelength in a wavelength range comprises: a graduatedtransmission filter, light source means for generating a beam of whitelight, means for passing said beam of white light through said graduatedtransmission filter, and means for cyclically displacing said graduatedtransmission filter relative to said beam.